Question: First consider the expression for: Take the product of $3$ and $x$ and add $8$. Now select the answer that matches the following: The sum of $7$ and the product of $3$ and that expression.
Solution: Let's break this problem into smaller and easier pieces. What is the product of $3$ and $x$ $3 \times x = \color{orange}{3x}$ What does adding $8$ to $3x$ do? $3x$ $ + 8$ What is the quantity of $3$ times that expression $3 \times (3x + 8) = \color{orange}{3(3x+8)}$ What is the sum of $7$ and $\color{orange}{3(3x+8)}$ $3(3x+8)$ $ + 7$ So the entire expression we're considering can be written as $3(3x+8)+7$.